1.

Approximate

correctly to two decimal places. Hint

2.

If v(t) = |10(t-1)²|-3, and s(0) = 5,

• complete the following table,explaining how you got your answers and why you know they're correct. For this part, you need not provide error estimates:
  

  t	0	1	2	3	4	5
  s(t)

• Use your data to sketch a graph of s(t).
• Use your graph of s(t) to sketch its derivative.
• Hint

3.

• Give the definition of

• Approximate

  using LEFT(N), for N=10,50, and 100.

• What do you think its actual value is? Hint

4.

Suppose that the rate at which a pollutant is being removed according to the equation dP/dt = -P₀e^-kt (in milligrams/liter/hour):

• Note: The derivative is negative, so pollutant is being added! (Alternatively, we could try to think of P as being the amount of pollutant left, but the interpretation was given to us, so we're stuck with pollutant being added...)
• If after 5 hours the rate at which the pollutant is being removed is 10% of what it was initially, what is k? Hint
• If the pollution level was originally 10 mg/liter, what is the pollution level after 5 hours? Hint

5.

For this problem we'll use the graph below twice:

• For this first part, suppose the graph above is that of position:
  • When is the position the greatest?
  • When is the velocity the greatest?
  • What would the average position be?
  • What would the average velocity be?
  • When is the acceleration positive? Negative?
  • Hint
• For this second part, suppose that the graph is that of velocity instead, and try to answer the same questions (the answers will be different!) Hint